Question

the exterior angles of a Pentagon are in the ratio 1:2:3:4:5.find all the interior angles of the Pentagon

Answer 1

Given ratio is 1: 2 : 3: 4: 5.

Let the exterior angles of a pentagon are in the ratio 1x,2x,3x,4x,5x.

We know that sum of exterior angles of a pentagon = 360.

1x + 2x + 3x + 4x + 5x = 360

15x = 360

x = 360/15

x = 24.

The exterior angles of the Pentagon are  24, 2(24),3(24),4(24),5(24) 

                                                                    = 24,48,72,96,120.


We know that sum of interior angles of a Pentagon = 180.

180 - 24, 180 - 48,180 - 72,180 - 96,180 - 120.

= 156,132,108,84,60.


Therefore the interior angles of a Pentagon are 156,132,108,84,60.


Hope this helps!

Answer 2

Answer:

let the exterior angles be x+2x+3x+4x+5x and this is equal to 360°( sum of exterior angles is 360°)

so,

x+2x+3x+4x+5x=360°

15x=360°

x=360°÷ 15

x=24°

and we know that sum of interior angle is 180°

x=180°- 24°

2x=180°-( 2×24°). =180°-48°

3x= 180°-(3×24°). =180°-72°

4x=180°-(4×24°). =180°-96°

5x=180°-(5×24°). =180°-120°

so,

x=156°

2x=132°

3x=108°

4x=84°

5x=60°

Answer.